The HOM interference has become a cornerstone of modern quantum technologies and widely utilized to characterize the single photons from solid-state emitter [1]}, [2]}, [3]}, [4]}, [5]} and the photon pairs from spontaneous parametric down-conversion (SPDC) [6]}, [7]}, [8]}. The HOM interference is also an important way to combine photons to implement controlled-NOT gate [9]}, [10]}, [11]} and to construct multi-photon entangled states including N00N states [12]}, [13]}, GHZ states [14]}, [6]}, [7]}, graph states [17]}, [14]} and multi-photon high-dimensional entangled states [19]}, [20]}, [21]}. The HOM interference is also the foundation of implementing the Bell state measurement, which is crucial for a variety of important quantum protocols, such as quantum teleportation [22]}, [23]}, [24]}, [25]}, entanglement swapping [26]}, [27]}, [28]} and connecting quantum nodes in quantum network [29]}, [30]}, [31]}, [32]}.
